The development of lawn moss is typically the result of a combination of factors: low soil fertility, compaction (and resulting poor drainage), excessive shade and moisture, too acidic a soil and finally, unhealthy or sparse turf. To conquer lawn moss successfully, you need to correct any and all factors :-)

Get a soil test to determine the pH of the soil underlying the lawn and if below around 6.3, apply lime as directed.

In addition to the annual aeration - which should lessen compaction - dethatch as well. Dethatching will remove a lot of the moss. After aeration, apply a thin layer of screened compost. And don't rake up the plugs - allow them to breakdown naturally. Increasing the organic matter that gets down past the lawn roots will also reduce compaction. And increase fertility.

Address any drainage issues. Lawns that ooze when you walk over them after a hard rain have drainage problems.

There's not much you can do about shade. Overseed with a shade tolerant seed blend or if too severe, consider replacing the lawn with a shade tolerant groundcover.

Keep the lawn as healthy as possible. Addressing all of the above is a start, but you may need to fertilize to increase or maintain soil fertility. A mulching mower and practicing 'grasscycling' will reduce the need for supplemental fertilizing and thatch buildup. Mow often and high, keeping the grass at about 2.5-3 inches. And practice careful watering - not too much, not too little. Too little watering in summer can also encourage the development of lawn mosses.

I sure wish my DH would let me get rid of the lawn. Why do many American males think a lawn is a status symbol? I'd much rather have moss paths around beds of plants. Neither our front nor back lawns grow well. Too much shade, too much compacted soil, too many tree roots. The moss and clover stay green but the lawn browns out...

Thanks gardengal- I have good drainage in the area, but will follow the other suggestions you provided. I fertilize twice a year with an organic fertilizer and have dethatched in the past. I just hate the way the lawn looks right afterwards! After aereation, how thin of a layer of compost should I add? The mowing has been a constant problem, as my husband insists on scalping it, even though I've told him time and time again to mow high. I'm pretty sure I'm watering correctly-deep but infrequent. I wish I could get rid of the lawn but our HOA requires 1000 sq. ft. in the front yard...

I see the development of a "mawn" as an improvement as you then have a low, bright green evergreen carpet without edging, fertilizing, mowing or watering. Here I have a heavy enough growth in some parts now it might be possible to spray and kill the remaining grass and weeds with glyphosate and eliminate mowing completely.

Bboy, I'm seriously considering the same thing. I have enough woodchips to bury my lawn several feet deep. Heck, I wouldn't even have to use glyphosate!
My problem is with moles. I used to trap them, but they came out of the woods as fast as I could eliminate em'. I finally gave up. I can live with woodchips for a few years with no mowing. The moles in the flower beds are a minor nuisance for me since I don't grow many real small plants.