Bobinôt is Calixta's husband and Bibi's father. He's described near the end of the story as the "embodiment of serious solicitude" (3.3), and that seems like a pretty fair summing up of the guy. Another word Chopin uses to describe Bobinôt is "stolid[ly]" (1.5) – that is, impassive or dull. How can someone "stolid" compete with someone as glamorous and flashy as Alcée? Seems like an unfair contest.
We know Bobinôt is kind and – oh this word again – full of solicitude. He brings Calixta a "can of shrimps" (1.5) because he knows she likes them. He takes good care of their son, whom he speaks to "on terms of perfect equality" (1.1) even though the boy is only four. He seems to be the strong, silent type.
The most he ever talks in the story is when he tells Bibi off for getting dirty on their walk home from the store. In Bibi's defense, a cyclone is bound to leave a bit of mud in its wake. Maybe Bobinôt's worry is part of a larger fear that Calixta might have run into trouble during the storm, or might be blaming them for not having been at home with her. That underlying worry might explain why, during the entire walk home, he works on "explanations and apologies which he had been composing all along the way" (4.5). He's right, in a way, that Calixta wasn't safe – left to her own devices, she had sex with another man.
While we're at it, let's talk about that infidelity. Even though the sex scene isn't about Bobinôt, he features in it by not being there. (Kind of a raw deal for Bobinôt, by the way. He's stuck at the store with their little boy and a "can of shrimps" [I.5], while his wife is experiencing the most passionate event of her life. Who wins on that one?) We can make some assumptions about Bobinôt and Calixta's relationship based on the way Alcée and Calixta are together. Chopin writes that when Calixta and Alcée have sex, "Her firm, elastic flesh. . . was knowing for the first time its birthright" (2.19). Ouch, Bobinôt. In all the years he's been with Calixta, she's never felt like that – never understood what her body was capable of or the kind of pleasure it could feel.
All in all, Bobinôt is a standup guy, but there's no doubt he's also kind of, well, boring. The kind of guy who makes for a good husband even if he's not that exciting in the sack.