I'm am in the middle of breaking my lease. My wife and I called our landlord to see if it was possible and he had agreed. About two weeks later (today) both he and his wife contacted us telling us he was now going to keep our security deposit and charge us rent for the time until he finds a new tenant. I understand that under Michigan law, it is legal to charge rent until a new tenant is found. I also know that security deposits are protected under the law from being used for any other purpose than repairs due to damage, and for back rent.

I did however do some research and found that my landlord has never registered the rental property with the city, and also has never pulled permits for electrical work that was performed on the house. I would like to know if I am still bound by my lease as at the time of, and up until now the house was never legal to rent in the first place.

I am not familiar with the registration law in MI, so answer generally. You should consult an attorney locally who can explain if that impacts your situation.
On a practical note, the landlord will need to inspect your unit after you leave and turn in the keys to be able to assess if there are damages that are to be withheld from the security deposit. So that is not something they can do now. You should leave a new address to send the unused security deposit to, or ask for an accounting of how the security deposit was used from the landlord and expect to receive this within usually 2-4 weeks after you move.