It is a very good idea to work together with plumbing and HVAC companies. I have done a fair amount of work like this, and there are no set rules.
First of all, I don't advertise together with them. Indeed, I don't advertise at all! One advantage of these informal partnerships is that your customers already know where to find you.
The most common situation is where one of use willact as the "prime" contractor on a job, and my price is part of the bid submitted. In these situations, depending upon the parties involved, I may be paid by the final customer, or by the other contractor. Either way, my price is the same.
Another situation arises when, say, the plumber is called to fix something- then discovers that the electrical is a mess as well. In that case, the plumber is actually my customer; I answer his call, and get paid by him.
One thing to remember about the second type of arrangement is that you will have to respond immediately....the plumber is there waiti ng for you!