Symbolism, Imagery, Allegory
The Davis family exists in what's called a line marriage. We can say two things for certain about this style of family building: It's an important symbol in The Moon is a Harsh Mistress, and anniversaries and the holiday season must be ridiculous in the Davis household.
During his trip to Earth, an inquisitive couple asks Mannie what a line marriage is (thanks for the info hook-up, you two). He explains that it means that people can opt in and out of the marriage, leading to generations of husbands and wives sharing each other. The husband and wife who have been in the marriage the longest are the senior husband and wife and head the household, and when they die or opt out, the next in line takes their place. Mannie also discusses other types of marriages on Luna, including polyandries, clans, and groups—though not in great detail.
During the discussion, he points out that there are several advantages to a line marriage, especially on a place like the moon where life is more difficult and death more likely. His list of awesome includes "financial security, fine home life it gives children, fact that death of a spouse, while tragic, could never be the tragedy it was in a temporary family, especially for children—children could not be orphaned" (18.127). We can see why he's so keen on it—community, security, co-parenting… not too shabby in our book.
To be clear, the point here is not to say that everyone should run out and get a line marriage right away. Rather, the idea is to expose readers to the possibility of exploring a type of marriage outside the traditional. The point is that there are options, and marriage can actually look any number of ways.
At one point in the novel, Prof asks the Luna Congress to not "reject the idea merely because it seems preposterous—think about it" (22.41). He is discussing politics at the time, but we think the same applies to the novel's exploration of marriages. Monogamous marriages seem natural to us because they are traditional, but could another type of marriage be better? The novel isn't saying it will be; it's only asking us to think about it.
For those who enjoy the mental exercise, don't forget to check out Heinlein's other novels, notably Stranger in a Strange Land. In that book, he creates another untraditional take on marriage through Mike's communal partnership. Again, the goal isn't to suggest this is better or worse—it's simply something to consider.