Not directly.

The way you would do it is
- one person pays (the person flying) and the other person pay them half back
Simplest would be credit card,
and you them pay his bank account or the credit card

That said, if you are taking turns to fly one way then the other..
the tickets are going to average out over time anyway..
and any small difference in prices (every 2 tickets) you can make up in meal costs etc. etc.

Seriously, the difference in costs of flights is going to be less than the costs of meals etc together.. and transport .. .and other costs while together ?? isn't it ?