This paper presents indoor penetration and reflection characteristics of common building materials at millimeter-wave (mmWave) frequencies. These channel properties are carefully studied at 60, 71, and 81 GHz using a narrow-band signal with directional horn antennas. We measured the reflection coefficients at these high frequencies with varying incident angles to the surface of a material. Average penetration loss of material is also studied based on antenna polarization effects (co-polarization and cross-polarization) at 73 GHz channel. Materials include drywall and plywood for these channel characteristics in an indoor lab environment. It is found that the co-polarization has a higher path gain of 45.4 dB in the line-of-sight (LOS) scenario as compared to cross-polarization for the 73 GHz channel. Moreover, average penetration loss of plywood is slightly increased for cross-polarization (8.96 dB/cm) as compared to the co-polarization antenna (8.10 dB/cm) penetration loss. Results show that reflection coefficients, | Γ ⊥ | are stronger at higher frequencies, and the range of | Γ ⊥ | varies from 0.38 to 0.83 with impinging direction (i.e., to the surface of drywall) for 20° to 60°, respectively, in the 81 GHz channel.