Yes, the base href does ignore the current directory. What indicated to me that you needed to go up one level is what you were actually getting:
mydomain.com/x/y.php
It all gets pretty confusing when we don't see the whole thing. It looked to me like you set the base href in the top page, then when you click to x, you are now at mydomain.com/x, so the current directory is appended to relative links within that page, unless you have also included the base href within x.php.
Anyway, I'm glad you got it working.