Thanks for the response JindrichP! I think you're right about keeping it simple. Sometimes I overthink things... And the more I think about it the more I agree that a shared resource pool is a simple and effective way to get the point across. It's a simple mechanic which will create the give and take type of dynamic that I'm looking for.
I'm not sure that I agree with having both characters share the same abilities though, I think it is important to have asymmetry between them. As the game progresses and the characters relationship is strained, the player will need to use more selfish abilities to stay alive. These abilities will help them fight off the zombies but also hurt the female character. I want the player to feel guilty about doing this to the other character. If the female character does it right back to the player then I think the player will feel like she is just a burden and won't feel bad about hurting her.
The idea of having the player character have a hulkish ability and having the female character have a healing ability is growing on me. I think there is a good balance of interesting gameplay and metaphorical meaning.
I'm thinking that maybe having a stress "resource" may be appropriate. The player character would hulk out after reaching a certain stress level, and the female character will gradually lose healing effectiveness as her stress level rises. Taking damage will increase stress level, and stress will decrease incrementally over time as long as the character isn't getting attacked. For the player, going hulk mode will reduce stress and cause the player to transform back to normal mode.
I feel pretty good about this idea but I am still open to any ideas, feedback or suggestions!