Question: Every of 5 previous brews (lager, pilsner, pale ale, IPA) have had a somewhat bitter and malty aftertaste to them. It's not too off-putting (except the lager) but is clearly there, yet not present on your tongue until swallowed (mostly aftertaste). *What would cause a beer to have this quality*?

5G brews. All liquid malt extracts. Different hop variations. VERY clean during brewing. Water is grocery store spring+distilled. Sugar/powdered(?) for carbonation before bottling. Dark bottles in closet 70-78d. Most have been nicely carbonated, slightly under ABV. Most the time a US-05 yeast is used. The temperature of fermentation have been slightly higher in the 70-78d range. Have done both 1 and 2nd fermentation rounds. Most fermentation times are 2-4 weeks plus 10-14 days in bottles. Nothing out of the ordinary for small-time brewers.

Answer: 
The "malty" taste can come from burning the sugars in the beer. When you slowly pour in the LME, vigorously stir the boil to avoid pooling on the bottom of the kettle.
what kind of hops and how much? You may need to increase the IBUs.

Also, what is the extract made from? Check to make sure it is a 2-Row and not something with more malt backbone (i.e. Pilsner)

You also may want to find a higher attenuation yeast strain.