Couple’s burial. Some prepare in advance a single burial plot intended for a couple, i.e., two meisim in one kever, one over the other. After they put the first meis in, they cover it with stone blocks, as is customary, and pour dirt on top. Then, they place blocks around within the kever and prepare a spot for a second meis. When the time comes, they reopen the gravestone to put the second meis on top.
Although we find that burying one meis above another was sometimes allowed in the past if there were six tefachim of dirt between the two bodies (שו''ע סי' שס''ב ס''ד ), this should be avoided l’chatchila for multiple reasons. Really, it is a departure from the accepted minhag; sometimes they are not careful about the amount of dirt between (עי' פתח''ת שם סק''ג ); and there are other reasons too (ס' משכן הנפש פכ''א אות ד').
Above-burial [קבורת על]. Another type of double burial is when there was kever intended for a single meis, but then they decided to add another meis, so they prepare the site to be able to hold another meis, e.g., a spouse or family member.
However, since the kever was not originally dug for two, they usually are not careful about the minimum space between the two. It is also disrespectful to the first meis to dig into the kever when that was not the original intention. They violate the issur of exhuming the dead, ר"ל; this is much worse than a couple’s burial that was originally intended to be that way.
Me’aras HaMachpeila. The Amora Rav holds Me’aras HaMachpeila was called so because there were couples buried there in two chambers, one further in than the other. Shmuel holds the cave itself had two sections, one on top of the other, like a house with an attic on top (עירובין דף נ''ג ע''א ). This was not a problem of having one meis above another in one kever, as the two caves were completely separate, and each meis was buried in the ground of its cave. The two were not buried in one kever.