Is it normal to be able to feel my heartbeat in my stomach?

Yes . See dr. Kwok's answer for a serious caution. But most people if paying attention - and if normal or slim - will be able to feel their aortic pulse. Especially at night when lying quietly.
Yes, but . . . A heartbeat or pulse can be felt in many places with certain activities. However, if a person feels a large pulsation in the stomach or abdomen (especially if he's been resting), the concern is an aneurysm of the aorta. If the aorta keeps enlarging and breaks open, the person will die. The aorta problem (AAA) is easily detected on an ultrasound scan, and is potentially fatal if not corrected.