You only ever hear of whales surfacing for a brief second to exhale/inhale before they dive back down. But do they ever just stay at surface level, laying there with their blow hole up in the air, continuously breathing for a while? One would think that might be a relaxing experience for them?
Whales often hang out on the surface for a while, for a number of reasons. Sometimes it is for curiosity, sometimes to socialize with other whales, and sometimes simply to rest. The particular sort behavior that you are describing sounds like logging, where the whale basically rests, often for an extended period of time, with its back slightly out of the water, looking sort of like a floating log.
From personal experience, I can attest to the fact that whales will hang out on the surface. Additionally, some species are more known among researchers/observers for this behavior. Kogia species (dwarf and pygmy sperm whales) are notorious for logging, for example. This study from Hawaii mentions that dwarf sperm whales spent a considerable amount of time in encounters either slow rolling at the surface or logging.