That is a two-pole AFCI breaker. Two-pole breakers will disable both poles when a fault is detected. It is likely that they are connected in a "shared-neutral" configuration, which is considered a single circuit. Half of the loads (outlets, lights, etc) would be connected to L1 while the other half of the loads are connected to L2. Even though the two hot wires share only one neutral wire, they can safely handle the same amount of power as two 15 A circuits with two neutral wires. Shared neutrals reduce the overall amount of wiring used (especially useful for long runs), but slightly increases the complexity of the wiring in the house.
It sounds like you may be mistaken as to how this is wired, or that perhaps I'm just not understanding your explanation. As others have mentioned, it's not possible to get 240 volts from a single pole in a 120/240V split phase system. Each tandem breaker provides 2 120 V circuits, this is true. However, if you measure between the terminals on a single tandem breaker, you'll get 0 volts. This is because the terminals are both powered from the same leg, and so are at the same voltage potential. If you measure from a terminal on the top tandem breaker to a terminal on the bottom one, then you'll measure 240 volts. This is because each breaker is connected to a different leg, which are each one half of a 240 volt circuit.
With all that said. For this setup to work, one appliance would have to be connected to both breaker. Something like this...
Notice that each appliance circuit has one wire connected to each of the tandem breakers. In this situation, you'd need a device like Speedy Petey shows.
![common trip device](https://i.stack.imgur.com/p304Y.jpg)
Which ties the breaker handles together, to provide common trip characteristics.
![enter image description here](https://i.stack.imgur.com/A9CJW.png)
Notice how the inner handles are tied together, and that the outer handles are also tied to each other. This way if either trip (or are turned off by the user), the entire circuit is shut off.
If this is wired the way you've explained, where the dryer is connected to the top tandem and the heater is connected to the bottom. Then there's some magic going on in those breakers.
Best Answer
No. The breakers are sized for the wire that was run. If you put two circuits into one breaker a single wire of the circuit (which was rated to carry 15amps) could now carry 30 before the breaker blows. This can lead to melting wires and fires.
You could combine both circuits to a single 15 amp breaker, but it would likely be overloaded. This might be a possibility if both circuits are very lightly loaded.
What you can do, if your panel supports them, is get a tandem breaker - which will have two 15 amp circuit breakers in a single unit that takes up the same slot as a single breaker.
Otherwise you will need an electrician to setup a subpanel - they will add a second panel which connects to the first, and move some of the circuits to this new panel to create room in the main one.