The e-m fields created by power lines don't affect the passage of e-m waves through the region around the power lines. [Technically a 'principle of superposition' operates, one of whose consequences is that beyond the region of the power lines, you couldn't tell that the e-m waves had passed through that region.] The interference you ask about is what you find when using a radio etc in the region of the power lines. The radio detects the fields due to the power lines and due to the e-m waves. What you hear may therefore not be what you want!