As the house is in the name of the wife, he cannot get benefit from the house. But he shall file an adultery case on his wife before the court and at the same time, he shall show proof if he purchased the house in his wife's name.
The house is in the name of wife, where she may not allow husband to reside/ use.
Whether the husband want to spoil his married life ? If so, he may collect all evidence(s) qua adultery and file a suit for a decree of divorce. Otherwise, husband should consult and engage a local prudent lawyer for appreciation of facts/ documents, professional advise and necessary proceeding.
Prima facie it is a hypothetical query vis-a-vis facts posted.
The wife in order to retaliate the husband's dictates especially when he chided or restricted or scolded her or prevented her from indulging in the acts of adultery discovered by him, she would have thrown him out of her house.
He cannot claim residential rights in such an event.
Instead, he can file a divorce case on the ground of adultery by producing clinching evidence of her acts of adultery and also by impleading the adulterer as second respondent.