That's EXACTLY what you're supposed to see.
You eyes cannot focus at separate depths at the same time, it's a physical impossibility.
Thus, when you focus on your finger, you'll see two images past your finger, and vice versa.
Try this to figure out which eye is truly dominant (unless you have an eye convergence problem, where you don't see in stereo, one eye should be dominant):
1. Pick an object in the distance, a stop sign, for instance. A few feet, a few yards, doesn't matter.
2. Make a circle with your thumb and index finger on one hand (an OK sign).
3. With both eyes open, sight the stop sign and focus on it through the circle you've made with your finger and thumb.
4. Close your left eye, and keep your right eye open. Can you still see the stop sign?
5. Open your left eye, and close your right eye. Can you still see the stop sign?
Your dominant eye is the one with which you could still see the stop sign when the other was closed.
If you TRULY don't have a dominant eye (which would put you in a significant minority of the population), you may want to schedule an appointment with an opthmalogist for a check up to make certain there isn't a problem. Seeing in stereo is pretty important.