A person doesn't have to be living with an alcoholic in order to budget arguements - its a universal problem for everybody.
The real danger in being financially mixed up with an alcoholic is the liability issue (IMHO). I think it would be wise for you to make whatever changes you think necessary, not only to keep the budget intact, but to protect you financially incase he has an accident, looses his job, etc. These changes might consist of not only having separate accounts, but also changing legal ownership of assests.
And, don't worry too much about him understanding your concerns about finances, because he won't. They are oblivious to the risks they are taking with their money as their health.