I would like to travel to France to visit my family, however the Greek ambassador has my Congolese passport to stamp a visa because I am going on holiday over there. But in the meantime I would like to go to France with my UK residence permit with my British husband and kids. Do I need my passport to travel or I can use my UK residence permit card?
There are two aspects to the answer:
1) EU rules require non-EU family members to carry a valid passport https://europa.eu/youreurope/citizens/travel/entry-exit/non-eu-family/index_en.htm
2) Even if you had your passport, you need a Schengen visa for France unless your residence card is a "Family member of an EU citizen" residence card. Can I travel to France without a visa?
So no, you cannot travel without your passport and your residence card alone is not sufficient if it was issued under UK national rules.