Recent observations of interplanetary medium (IPM) atomic hydrogen Lyman-{alpha} (Ly{alpha}) emission in the outer solar system, made with the Alice ultraviolet spectrograph on New Horizons (NH), are presented. The observations include regularly spaced great-circle scans of the sky and pointed observations near the downstream and upstream flow directions of interstellar H atoms. The NH Alice data agree very well with the much earlier Voyager UVS results, after these are reduced by a factor of 2.4 in brightness, in accordance with recent re-analyses. In particular, the falloff of IPM Ly{alpha} brightness in the upstream-looking direction as a function of spacecraft distance from the Sun is well-matched by an expected 1/r dependence, but with an added constant brightness of ~40 Rayleighs. This additional brightness is a possible signature of the hydrogen wall at the heliopause or of a more distant background. Ongoing observations are planned at a cadence of roughly twice per year.