Photoshop: Remove Zero Pixel Boundary Between Layer Selections

If I select a subject using no feather (or 0.2 pixels), create a new layer with it (cntl J), then select the new layer together with the old one, and then deselect the new one, I obtain marching ants for the subject on the orginal layer. If I then delete within the selected area, I get one layer with just the background, and a second layer with just the subject. If I then make both these layers visible, but no others, I see a zero pixel outline between the two (even with no feathering, as I said). I want to get rid of this, as it's causing problems when I want to blur only the background, as it gives messy edges. How do I achieve this?