Here's a diplexer I built about 20 years ago (time flies when you're
having fun). It allowed me to transmit on 146 MHz FM using about 10 Watt
& at the same time listen to AM & (more surprisingly) FM radio. The AM/FM
radio emitted a click as I hit the transmit button, but otherwise worked
fine.

This diplexer has outlived two cars & co-existed peacefully with AM/FM
radios in both. It allowed me to play ham radio without driving around
under a mobile aerial farm.
It is currently awaiting the purchase of another car.

The diplexer is guaranteed to be environmentally friendly and completely
invisible to YLs & XYLs. (and it doesn't contain PCBs ;-)

The only disadvantage is that you will have to adjust it for:
1.  Minimum feedthrough to the AM/FM radio &
2.  Best SWR (better than 1.2:1 in my case) &
3.  The AM antenna trimmer on the radio will need to be re-peaked
    for best reception in the upper part of the AM broadcast band.

73, de Phil Rice VK3BHR
from the land of OZ (Australia)

PS  Have fun. ASCII art follows.....

  \|/
   |
   |
   |          C          < 0.25 wavelength >
   +----------||-------=========================>> 50 Ohm coax to 146Mhz. rig
   |                   ||                   ||
   |                   ||                   ||
   +----               ||                   ||    Stub lengths adjusted
   L    |              ||                   ||    to minimise SWR
   L   === C           S/C                  ||    See ARRL or RSGB handbooks
   L    |                                   ||    for "Two Stub Tuner"
   +----                                    ||
   |                                        S/C
   |
   +--------+----+----->> to AM/FM Car radio
   |        |    |
   L        |    |
   L        |    |
   L        |    |
   |        |    |      All C's are about 10 to 15 pF air spaced trimmers
   |       ---  ---     (not too high or the AM tuner gets deaf at 1.6 MHz.)
  === C    \ /  / \     The L's are about 6 turns, 0.25 inch ID 0.5 inch long
   |       ---  ---     Both the series & parallel tuned circuits are resonant
   |        |    |      at 146MHz
   +--------+----+      Diodes are 1N914's just in case some RF sneaks through.
   |
 -----
  ---
   -