The highly irradiated transiting exoplanet, HAT-P-7b, currently provides one of the best opportunities for studying planetary emission in the optical and infrared wavelengths. We observe six near-consecutive secondary eclipses of HAT-P-7b at optical wavelengths with the EPOXI spacecraft. We place an upper limit on the relative eclipse depth of 0.055% (95% confidence). We also analyze Spitzer observations of the same target in the infrared, obtaining secondary eclipse depths of 0.098% ± 0.017%, 0.159% ± 0.022%, 0.245% ± 0.031%, and 0.225% ± 0.052% in the 3.6, 4.5, 5.8, and 8.0 μm IRAC bands, respectively. We combine these measurements with the recently published Kepler secondary eclipse measurement and generate atmospheric models for the dayside of the planet that are consistent with both the optical and infrared measurements. The data are best fit by models with a temperature inversion, as expected from the high incident flux. The models predict a low optical albedo of 0.13, with subsolar abundances of Na, K, TiO, and VO. We also find that the best-fitting models predict that 10% of the absorbed stellar flux is redistributed to the nightside of the planet, which is qualitatively consistent with the inefficient day-night redistribution apparent in the Kepler phase curve. Models without thermal inversions fit the data only at the 1.25σ level, and also require an overabundance of methane, which is not expected in the very hot atmosphere of HAT-P-7b. We also analyze the eight transits of HAT-P-7b present in the EPOXI data set and improve the constraints on the system parameters, finding a period of P = 2.2047308 ± 0.0000025 days, a stellar radius of R = 1.824 ± 0.089 R _☉, a planetary radius of R_p = 1.342 ± 0.068 R _Jup, and an inclination of i = 85.7^+3.5 _–2.2 deg.