laying 1 object on top of another without sinking to build plate

I designed a housenumber and name sign. I want to print a background of 1.5mm in black and a detailed forgound with small unconnected elements in white on the foreground. Also 1.5 mm.

When i try to assemble the objects i end up with the foreground sunk into the background.

I also tried to move the background below the build plate before assembling, but i can not move it further down than about half.

Anyone have a solution? Or a link to a solution?

Greetz,

Rik Lijkendijk