Conventional binocular head-mounted displays (HMDs) vary the stimulus to vergence with the information in the picture, while the stimulus to accommodation remains fixed at the apparent distance of the display, as created by the viewing optics. Sustained vergence-accommodation conflict (VAC) has been associated with visual discomfort, motivating numerous proposals for delivering near-correct accommodation cues. We introduce focal surface displays to meet this challenge, augmenting conventional HMDs with a phase-only spatial light modulator (SLM) placed between the display screen and viewing optics. This SLM acts as a dynamic freeform lens, shaping synthesized focal surfaces to conform to the virtual scene geometry. We introduce a framework to decompose target focal stacks and depth maps into one or more pairs of piecewise smooth focal surfaces and underlying display images. We build on recent developments in "optimized blending" to implement a multifocal display that allows the accurate depiction of occluding, semi-transparent, and reflective objects. Practical benefits over prior accommodation-supporting HMDs are demonstrated using a binocular focal surface display employing a liquid crystal on silicon (LCOS) phase SLM and an organic light-emitting diode (OLED) display.