Using the Short Wavelength Spectrometer on the Infrared Space Observatory, we measured in the Orion Nebula several components of the He I Brα transition, the first detections to the best of our knowledge in an H II region, and the H I Brα line. A value of He⁺/H⁺=0.085±0.003 is inferred from these data and is typical of previous values found for Orion. The IR method to obtain He⁺/H⁺ is very insensitive to extinction. The measurement of the weak He I 2.855 μm (5p ³P^o→4s ³S) flux permits an assessment of T_e in the He⁺ region. Its flux relative to the flux of He I 4.0490 μm (5g ³G→4f ³F^o, 5g ¹G→4f ¹F^o blend) is roughly T_e (for T_e range applicable to most H II regions and planetary nebulae) and depends little on N_e. From our measured ratio, using N_e = 10⁴ cm^-3, T_e is slightly less than 10⁴ K. We stress that many IR measurements of a hydrogen line are likely to also include one or more significant helium line contributions. Attributing all of the flux to the stronger H I line will result in underestimates for abundance ratios relative to H⁺. This has usually not been taken into account in the past when deriving abundances of other ions/elements relative to H. Errors in the velocity and line width inferred may also occur by failure to consider the blended He component. Because the strongest He I lines will generally be on the blue side of their counterpart H I line, interpreting a blended feature as only H I will cause a spurious bias to lower velocities.