Two-headed bosses are common when people work for businesses founded by relatives, which, I am sure, can be a source of fascinating undercurrents and rivalries. I invite my readers to share relevant stories.
I, on the other hand, worked (more than once) for equal partners who were not related. Each of the duos consisted of individuals so different, it was a miracle they stayed in business together. As a CFO, forced into the middle of the co-owners dynamics, I was able to observe common behavioral tendencies in the bosses themselves and people around them.
Business partners' alliances are usually symbiotic. One is an idea generator, the other is an implementer. One is brains, the other is money. One can close a deal in seconds, the other makes sure the company performs. They always complement each other, or they wouldn't be in the trenches together.
Either will squeeze all juices out of you, and yet their personalities differ just as much as their abilities. One is usually more diplomatic, better with people, logical, frugal. The other is brash, careless, erratic, a lavish spender. They don't see eye to eye about the majority of business issues and frequently talk to their CFO or Controller separately, presenting contradictory positions.
260 years ago, in "The Servant of Two Masters," Carlo Goldoni depicted the delirium of working for two employers who try to find each other without knowing they live in the same hotel. Sounds familiar? Poor Truffaldino is so anxious, he develops a stutter. Imagine the hilarity! Well, at least he got double wages. When your single-salary job depends on maneuvering two conflicting bosses, you don't feel like laughing.
Most people end up aligning themselves with one of them. Sometimes, it works out in a natural way: if one owner oversees Production, while another spearheads Sales and Marketing, it is obvious where VP of Ops and VP of Sales allegiances will lie.
Even when it's not clear-cut, people have a tendency to navigate with their issues toward the boss who is perceived to be "nicer," regardless of his preparedness to make relevant decisions. As the result, you may end up with a wrong solution, or the issue is brought to the other owner's attention anyway; only now he knows that you tried to bypass him. Either way, you are screwed.
CFOs and Controllers should not form any alliances when they work for two partners. When monetary matters are concerned, both must be kept in the loop. In super-important cases, get them into the same room, whether they like it or not. I am known for bringing bosses into the office from their summer residencies in the middle of July, when I had to.
Of course, you have to earn your right to do so with hard work and authoritative success. You also need to be very diplomatic with both of them - either must think you prefer deal with him and inform the other out of courtesy. It takes Machiavellian skills to boss the bosses. Otherwise, you will end up stuttering, like poor Truffaldino.