Here laughter and tears are both used as a metaphor for "normal family problems, some of which are horrible and some just funny." The idea is that dysfunction is common and this family argues and has problems, which is also normal.
We are like/similar to/you might call us a dysfunctional family.
The author is probably exaggerating, and is referring to squabbles and fallings out and fights that go on in his family, as well as the good family times they share together: the tears and the laughter.
Real dysfunctional families manifest great conflict between family members, antisocial behaviours, and physcial and emotional abuse - usually alcohol-fueled. Many tears, but no doubt, some laughter, even if at the expense of some other family member, or as part of their antisocial irresponsibility. Setting a cat on fire would be hilarious.