Photodissociation cross sections and absorption coefficents of the He2(+) molecular ions for transitions from the Chi (2)Epsilon(+) ground state to the vibrational continuum of the A (2)Epsilon(+) excited state have been determined for photon wavelengths lambda between 50 nm and 20 microns and for temperatures T between 4200 and 50,400 K and between 3150 and 25,200 K, respctivley. The cross sections are obtained through a fully quantum-mechanical method, and it is shown that inclusion of the high-lying rotational states is important for determination of the correct long-wavelengthh cross section amplitude and the peak wavelength. Free-free absorption coefficients are also obtained using the semiclassical method of Bates. The detection possibility of He2(+) and H2(+) in cool white dwarfs is dicussed and shown to be insignificant. An effectively temperature independent cutoff in the He2(+) photodissociation cross section in the EUV at approximately 60 nm appears to be the only possible observable feature. It is suggested that He2(+) may be responsible for an observed UV flux deficiency in some cool DB stars as well as in the DZ stars WD 0552 - 041 and WD 1334 + 039. We further suggest that the star WD 0752 - 676 currently assumed to be helium-rich may actually have a hydrogen-dominated atmosphere.