I think a lot of people replying to this are close but don't quite hit all of the points together. The Chesapeake Bay Bridge-Tunnel is 23 miles long and it goes from the southern tip of the peninsula in Maryland to the Virginia beach area. The engineering of a roadway that traverses such a distance was unprecedented.

The Bay Bridge-Tunnel is a combination of trestle bridges, truss bridges, and tunnels. There are actually pairs of two lane bridges that feed into a tunnel at two locations in the bay. The picture honestly does not do the structure justice. Due to the length of bay that needs to be crossed a single span bridge that would accommodate shipping traffic would not be possible (The longest suspension bridge is about 2.5 miles long in Japan).

The Chesapeake Bay is the entrance to more than one major port on the east coast and therefore a draw bridge(s) would not work practically due to the high traffic of the waterway.

In conclusion, the best solution was a combination of bridges and tunnels to allow for the passage of cars across the bay while still accommodating shipping traffic that goes above tunnels at two points. The only other crossing is about three hours North and you'd have to travel through Washington DC and Richmond before getting to Virginia Beach.