"I have two brothers and three sisters..." - immediate family

The vocabulary for immediate family members starts out easy, then gets trickier:

We'll start with "family." Latin familia actually referred to the family's property (including the slaves). (Domus, like domestic, was the word for family.) Nonetheless, the Romance languages adopted it to refer to shared kinship with Sp. familia, Fr. famille and It. famiglia.

In the familia, one found pater et mater (father and mother), who became Sp. padre y madre, Italian padre e madre and French père et mère. Related: paternal and maternal, i.e. fatherly and motherly.

The parents were called parentes or genitori in Latin. For Romance we have Spanish los padres, French les parents and Italian i genitori. Parents and padres should be clear; for genitori, think of gene, generation and (the highfalutin word for parent) progenitor.

If you're going to have parents, you need children. Lat. infantes becomes Fr. les enfants (cf infants). In Italian, they're i bambini, the babies. In Sp. it's los niños. (I'm not sure of the origin; possibly it's the same as "ninny", an innocent.)

For children, you might have a son and daughter - Lat. filius et filia become It. figlio e figlia, Fr. fils (feess) et fille (feey), Sp. hijo y hija (and yes, even the Spanish is easily derived from the Latin if you know the sound change rules, see the "Sound Correspondences" page).

A son and daughter will, of course, be brother and sister - Lat. frater et soror become Fr. frère (just as pater becomes père) et soeur, It. fratello e sorella (which are diminuitive forms, i.e. "little bro' and little sis"). In Sp. it's hermano y hermana, from Lat. germanus - shared parentage (think of "germination").

Finally, in charge of this all, we have man and woman, husband and wife:

Lat. homo gives Sp. hombre, Fr. homme, It. uomo = man

From here it gets complicated:
woman: Lat. mulier (woman, wife) > Sp. mujer. Lat. domina (lady) > It. donna. Lat. femina (female) > Fr. femme.

husband: Lat. maritus (husband, cf marital) > It. marito, Fr. mari. Lat. sponsus (bridegroom, promised) > Sp. esposo.

wife: Lat. femina > Fr. femme. Lat. mulier > It. moglie. Lat. sponsa > Sp. esposa.

Whew! I hope you didn't actually learn all the vocabulary from reading that. But now you've got enough background that this will sink in more readily:

(English = Spanish, French, Italian)
man and woman = hombre y mujer, homme et femme, uomo e donna
husband and wife = esposo y esposa, mari et femme, marito e moglie
father and mother = padre y madre, père et mère, padre e madre
parents = los padres, les parents, i genitori
children = los niños, les enfants, i bambini
son and daughter = hijo y hija, fils et fille, figlio e figlia
brother and sister = hermano y hermana, frère et soeur, fratello e sorella