$n$ cities with two ways

You cannot have $n \lt 3$ to satisfy the existence of a plane direct connection and a car direct connection.

For $n=3$ you are going to have three direct connections, two of a particular type and one of the other. The first type of connection connects all the cities directly or indirectly.

For $n \gt 3$, given A and B, take any two other cities. Between these four cities there are six direct connections. So at least three of the direct connections are of a particular type. This particular type directly or indirectly connects all four cities, except when it forms a triangle between three of them and the other type provides direct connections between the fourth city and the other three. Therefore in every case the four cities are linked directly or indirectly by a single type of connection. This picture may help when there are at least three black direct connections:

So you can get between any two cities on a single type of connection, passing though at most two other cities.