The structure of whipped cream is very similar to the fat and air structure that exists in ice cream. Cream is an emulsion with a fat content of 35-40%. When you whip a bowl of heavy cream, the agitation and the air bubbles that are added cause the fat globules to begin to partially coalesce in chains and clusters and adsorb to and spread around the air bubbles.
As the fat partially coalesces, it causes one fat-stabilized air bubble to be linked to the next, and so on. The whipped cream soon starts to become stiff and dry appearing and takes on a smooth texture. This results from the formation of this partially coalesced fat structure stabilizing the air bubbles. The water, lactose and proteins are trapped in the spaces around the fat-stabilized air bubbles. The crystalline fat content is essential (hence whipping of cream is very temperature dependent) so that the fat globules partially coalesce into a 3-dimensional structure rather than fully coalesce into larger and larger globules that are not capable of structure-building. This is caused by the crystals within the globules that cause them to stick together into chains and clusters, but still retain the individual identity of the globules. Please see a further description of this process for details. If whipped cream is whipped too far, the fat will begin to churn and butter particles will form.
Below are scanning electron micrographs image of whipped cream. If you compare the schematics above with the "real thing" below, you should be able to fully understand whipped cream structure.
The structure of whipped cream as determined by scanning electron microscopy. A. Overview showing the relative size and prevalence of air bubbles (a) and fat globules (f); bar = 30 um. B. Internal structure of the air bubble, showing the layer of partially coalesced fat which has stabilized the bubble; bar = 5 um. C. Details of the partially coalesced fat layer, showing the interaction of the individual fat globules. Bar = 3 um.
Fat partial coalescence as it affects things like whipped cream and ice cream structure is an active area of our research here at the University of Guelph. Please see my publications for more details of our research.