
Szeps was born in Lausanne, Switzerland. Due to the German invasion of Poland, his parents fled to France. His father left the family to join the French Resistance, and his mother and three-year-old sister made their way to a refugee camp in Lausanne, where Henri was born. He spent a lot of time with foster families, and later at a French orphanage, before coming to Australia at the age of eight with his mother and sister.
Szeps is probably best known for his role as selfish dentist Robert Beare in the classic Australian television comedy series Mother and Son (1984 to 1994), with Garry McDonald, Ruth Cracknell and Judy Morris. Another prominent role was in Palace of Dreams for which he received a Penguin Award. He played the Doctor in the world première of David Williamson's play, Travelling North, and was asked to repeat the performance in the 1987 film, with Leo McKern & Graham Kennedy.

South Pacific
2001 · as Benoit

Vietnam
1987 · as Harold Holt

Now and Forever
1983 · as Barry York

The Return of Captain Invincible
1983 · as Chief Security Officer

The Plumber
1979 · as David Medavoy

Edge of Power
1989 · as Steve Traynor

Travelling North
1987 · as Saul

Fatty Finn
1980 · as Mr Zilch

You Can't See 'round Corners
1969 · as Peter

Seeing Red
1992 · as Louie Leeds

Do I Have to Kill My Child?
1976 · as Doctor

The Girl From Moonooloo
1983 · as Bert

A Tale of Two Cities
1984 · as voice

Les Patterson Saves the World
1987 · as Charles Herpes

Sherlock Holmes and the Valley of Fear
1983 · as (voice)

Warming Up
1985 · as Sergeant Peter Sullivan

The Best of Friends
1982 · as Lilo

Sherlock Holmes and a Study in Scarlet
1983