Other cultures practice polyandry (multiple husbands), and there's a whole mess of other possibilities, for example the "line marriage" that Heinlein describes in "The Moon is a Harsh Mistress," which arguably yeilds an even stronger family than the usual 1man-1woman marriage.
What makes you think that the government needs to be involved in fostering strong families, anyway? We had families for hundreds of years before we had a strong central government, and arguably, the reason we don't generally have strong families anymore these days is precisely because of government intervention, not for the lack of it!!
No-fault divorce laws seriously damaged the contract of marriage, rendering virtually meaningless a breach of that contract, and government's welfare policies that are designed to keep the poor in their place and dependant on government, instead of on themselves and the family unit, did the rest.
If someone wants to get married and there's no more tax benefits (or penalties) and legal presumptions based on marriage, and the government no longer licenses and registers marriages, people are still going to get married anyway, still going to buy a house together, still going to have kids together.
I can't fathom why people think that because two men want to enter into a marriage-like contract it poses a threat to the usual form of marriage and family.