The relationship between Jimmy and Alison can reasonably be described as fraught. This is largely because of Jimmy's insecurities. His lowly status in British society does not match with his intelligence or level of education, so he regularly takes out his frustrations on Alison.
As someone from a relatively privileged background, Alison forms what for Jimmy is the ideal target for all his pent-up hatred towards a class-conscious society that does people like him no favors. He can't hit back at society, but he can, and does, hit back at Alison as the representative of that society and all it stands for.
Jimmy, then, is what we would now call a domestic abuser. By constantly criticizing Alison and subjecting her to verbal abuse, he's treating his wife with contempt and disrespect, exactly the same way that he believes he's been treated by society. Jimmy further disrespects Alison by cheating on her with her friend Helena. Jimmy's philandering is further proof, if it were needed, of his irredeemable misogyny.
Despite all of this, there does seem to be genuine love in this relationship. It's just that this love tends to be obscured by Jimmy's insecurities and his need for Alison to experience the kind of hurt and emotional pain he has endured throughout his life.