The oldest, most correct form, is to have a write-in lie on the invitation itself where you write in the names of the couple and any minor children who are invited, using the correct form of their social names which is generally their title and surname only (title and firstname only for sons and younger daughters). Like this:
Mr and Mrs Firstname Goodhost
request the honour of the company of
Mr and Mrs Phipps
Master Aloysius, Miss Phipps, and Miss Aspasia
Nowadays most people would leave off the title for the children and just use their first names.
When you have all the names on the invitation itself, you put it in an envelope and address it just to the lady of the house (except in the USA where it’s correct to address it to both members of a couple equally). Envelopes going through the mail use the addressee’s business name, which is their title, first name, and surname.
The next-most-correct method, used when you have your invitations engraved with the line “request the honour of your presence” so as to avoid having to write on the invitation itself, is to use two envelopes: you write all the names just as shown above on one envelope with no house-address and put the invitation in that (the “inner envelope”); and then you put that whole invitation into a slightly larger envelope that you address just to the lady of the house (or in the US, to the couple) and stamp and mail that “outer envelope”. That way your guests still get addressed personally by name and still know exactly who is invited, but you aren’t advertising the identity of minor children to the letter-carrier and every paedophile who might rifle through your guests’ mailbox while they are out.
Nowadays many people think the inner envelope is a waste and do without it. If that’s your opinion then the next-best choice is to write in the names on the RSVP card just as shown above, and still address the envelope only to the adults. Personally, I’d go with the write-in line on the invitation and do without the RSVP card as well, since they’re even more of a waste and aren’t really proper form themselves, but if you already have your invitations done and already have the RSVP cards, this is a good option.
Of course, if any of those children are already “out” socially (which usually means eighteen and over, legal adults) they should get their own invitation, but you can put it in the same outer envelope as their parents’ invitation.