Passion for the public and for show business was already a characteristic of Eunice’s family. Her grandparents, her mother – Júlia Muñoz (Mimi) – and her uncles formed a theatre company that performed in the provinces and was known as the "Carmo Troupe".
Mimi met, in Alter do Chão, Hernâni Muñoz who was one of the attractions of the Muñoz Circus, dancing to perfection a tango with his sister Alzira.
They married in 1927, and the following year their first child was born, Eunice Muñoz, followed by her brother Hernâni in 1929.

Later this family will form its own company, in which Eunice performed since the age of 5, showing great musical intuition while singing popular songs that were fashionable at the time.

When doing variety shows in cinemas became unviable, the family launched the "Teatro Desmontável" of Mimi Muñoz. This meant that Eunice’s studies were carried out according to the family’s tours. She went to high school in Fornos de Algodres, where her parents retired from that activity and dedicated themselves to training small variety theatre groups, becoming theatre managers.

Eunice Muñoz went on stage for the first time to interpret the role of Isabel, in the play "Vendaval" (Storm), showing at the Teatro Nacional D. Maria II, by the Rey Colaço Robles Monteiro Company, on the 28th of November, 1941, as a result of a recommendation made by Sales Ribeiro to Amélia Rey Colaço. He advised her to have four girls supporting Maria Lalande in this play, which would be the last by Virgínia Vitorino. In this play, Eunice draws the attention of João Villaret and awakens the interest and admiration of Amélia Rey Colaço.

After an interval, Eunice returns to the National Theatre in 1942, joining the Rey Colaço Robles Monteiro Company and performing side by side with the most important actors of that period in Portugal.

During the company’s summer holiday, she was called to perform beside Estevão Amarante in the operetta "João Ratão", at the Teatro Avenida. That same summer, she played a role in a comedy at the Teatro Variedades, "Raparigas Modernas" (Modern Girls). The performance she gave while playing "Maria" in the play "Frei Luís de Sousa" staged by the Rey Colaço Robles Monteiro Company, increased her prestige as an actress.

            Pormenor de fotografia da Troupe CarmoFotografia de Hernanin Muñoz e sua irmã AlziraFotografia de Eunice Muñoz actuando com 4 anosPormenor do teatro desmontável Mimi MuñozFotografia do espectáculo 'Vendaval', Companhia Rey Colaço Robles Monteiro, Teatro Nacional D. Maria II, 1941Fotografia do espectáculo 'Frei Luís de Sousa', Companhia Rey Colaço Robles Monteiro, Teatro Nacional D. Maria II, 1943

She left the National Theatre in the summer of 1944 and, given her talent and great capacity, she went from playing sentimental comedies to farces and operetta. This led her to play important roles.

On the 24th of July, 1945, Eunice passed her final exams at the Conservatory playing the 2nd act of "Vivette", and getter extremely good marks. That very night, her name was featured with the same degree of importance as those of the well-known actors Mirita Casimiro and Vasco Santana on the poster for the opening of the musical comedy "Chuva de Filhos" (Rain of Children).

This cycle in the life of Eunice close on the 23rd of April 1946, with the farce "Cuidado com a Bernarda!" (Be Careful with Bernarda!), and her first role in the cinema in the film "Má Fortuna" (Ill Fortune), which opened on the 23rd of September. She played a noble woman who has an unrequited passion for Camões, a role that won her the prize of best actress awarded by SNI. She was only 17 years old.

In 1947, Eunice married architect Rui Couto and declared, in interviews given to several magazines, that she wanted to exchange the theatre for the cinema.

                  Fotografia do espectáculo 'Chuva de filhos', Teatro Variedades, 1945.Fotografia de Eunice Muñoz no dia do casamento com Rui Couto, 1946Fotografia do espectáculo 'Outono em flor', Companhia Rey Colaço Robles Monteiro, Teatro Nacional D. Maria II, 1949Fotografia do espectáculo 'Noite de Reis', Teatro Nacional Popular, Teatro da Trindade, 1956Fotografia do espectáculo 'As criadas', Teatro Experimental de Cascais, Teatro Gil Vicente, 1972

She participated in another film, but reappeared on stage in November of that year, playing the main role in the play "A Noite de 16 de Janeiro" (The Night of the 16th of January).

In 1949, she performed again with the Rey Colaço Robles Monteiro Company in the play " Outono em Flor" (Autumn in Bloom), the last play by Júlio Dantas.
That year, the actress almost reached breaking point with the profession. She made another three films, before a 15-year interval in her cinema career. At that time, Eunice was not working in vaudeville theatre, but she would be a huge success in 1951, with the company formed under the direction of António Pedro, in Teatro Ginásio, interpreting roles in national and international plays.

Playing at the Teatro Trindade in the play "João da Lua", Eunice then left the profession that has almost been imposed on her.
She then went to work in a cork shop, where she was at the till.
Her return to the stage took place on the 9th of November 1955, at the Teatro Avenida.

The birth of a son also led to another interval that lasted until 1957, when playing at the Teatro da Trindade, she joined the theatre company Teatro Nacional Popular, formed by Francisco Ribeiro. She had a role in the play "Night of Kings" by Shakespeare.
In 1965, Eunice accepted the challenge to join the Companhia Portuguesa de Comediantes with two daily performances and a matinee on Sundays.

In 1969, Eunice’s disillusion with the state of the theatre at the time led her to form a company with José de Castro, named "Somos Dois" (There’s Two of Us) which was to carry out a long tour in Angola and Mozambique.
In 1971, she jointed for the last time the Rey Colaço Robles Monteiro Company.

The Teatro Experimental de Cascais once again was the stage for one of Eunice Muñoz’s great successes in the play "The Maids" by Jean Genet, which was succeeded by a long tour of Africa.

She came back to Lisbon in May 1974 and she only returned to the stage in 1976.

There were further absences followed by the inevitable return to the stage to play various types of dramatic roles in the career of this actress who is, "undoubtedly the youngest and most daring of Portuguese actresses."