Why might a 1995 Honda Civic shake at 60 MPH even though the tires are balanced?

It is very likely front end out of alignment or the tie rod ends being bad or both.

i disagree - probably the tires are out of balance still or again - very rare for wheel misalignment to cause a shake - tie rod end shake would probably occur more frequently

get over 60 mph - put in neutral and see if shake still exists - thatll eliminate drivetrain possibilities

likely culprit: tires or rims - have looked at again

I agree with this answer 100%, alignment DOES NOT cause vibrations, go with the likely culprits

I agree, alignment is not a problem. Tie rods will cause a side-to-side vibration in the steering wheel and sometimes the body. Bad shocks will cause an up-and-down vibration in the whole vehicle, expecially on a rough road. A bad tire, i.e. one with a tread separation, will cause slight to severe vibration, and will still balance OK. I also once had a problem with an improperly installed wheel weight which fell off 5 miles after having the tires balanced.

What they said above is most likely the answer. I will also just throw out that it could be something as simple as the lug nuts are not fully tightened. Its hard to trust a dealer or mechanic.

My husband was having the same problem and it just kept getting worse. The problem was his '95 Honda Civic had a bad CVC joint and boot. It causes the car to shake badly. It will also cause the car to go out of alignment quickly. We are having to replace both front tires and the front right axle because of it. His car would start shaking at speeds of 75 mph or more. It just started shaking at the speed limit of 55-65 mph today. If this is your problem you might want to get it fixed before it gets worse.