No complaint is maintainable.
Whether the chat history or even if you personally happen to see they both living together or indulging in any compromising activities, no complaint with the police or any law enforcing authority would be maintainable nor your complaint would be entertained.
Don't act on any misguidance or wrong interpretation of law.
The supreme court itself has clearly stated that it is the will and wish of two individuals to have relationship outside their marriage, which cannot be restricted hence the particular provision of law in the Indian penal code had been repealed by a judgment by supreme court.
If you do not want to adjust or digest your husband's this character, you are at your liberty to file a contested divorce case on the grounds of cruelty citing his acts of adultery as reason for your mental cruelty