I have been laying mines to check their effectiveness as a defense.  So far they are a waste of resources and time. 
Minelayers can only put down one mine per turn. 

And a high level infantry unit can pass right through 2 mines and still be healthy. 

In the screenshot below there were two mines. One where the infantry is and one where the jeep landed.
The infantry walked through two minefields and doesn't have a scratch.