Playing with DepthBias render state do not give any results...
I still assume it's a z-fighting problem. And I assume you're already using LessEqual for the ZFunc (this should be the default).
Oh my, I just realized this: Depth Bias (Direct3D 9). The devil's in the details:
The bias is not applied to any line and point primitive. However, this bias needs to be applied to triangles drawn in wireframe mode.
Alternative: Setup your WorldViewProjection to manually create a depth bias, e.g. use WVP * Matrix.Translation(0,0,-0.001f) or something. Edit: For the lines only!