Comedy
All the good characters we like get married and all the bad characters either die or are sent packing. That's a pretty good indication that we're reading a comedy.
But we don't necessarily know it from the beginning, because for all its happy endings, Our Mutual Friend also contains its fair share of murder and violence and (shudder) taxidermy.
Dickens' descriptions of uppercrust British society also make it a fairly satirical novel at times, too. But ultimately, the broad category of "comedy" is the only one large enough to shoulder the full weight of Dickens' multiple storylines… as well as the feel-good ending of this doorstop of a novel.