This paper reports measurements of self-interference (SI) channels in an in-band full-duplex (IBFD) relay scenario for millimeter-wave street-level backhauling. The street-level backhauling suffers from clutters surrounding the relay devices and hence SI originating from the environment may be dominant. An ultrawideband channel sounder operating at 70 GHz carrier frequency is used to measure the SI channels in a chamber, indoor window-side, indoor and outdoor corner scenarios. The transmit and receive antennas are waveguide-fed lens antennas. The measurements showed that cross-polarized feeding of waveguides to the lenses provided higher isolation than co-polarized feeding. In the corner scenario, observed minimum isolation level is 85 dB in the frequency domain, and 100 dB in the delay domain. The results confirmed that isolation is not limited by the direct coupling because of the high directivity of the lens antenna, but by the environmental coupling. Further link budget analysis for outdoor-to-indoor backhauling showed that the IBFD relay with practical transmit power is capable of enhancing the signal-to-noise ratio and hence extending the coverage, as SI at the relay receiver can be almost the same level as thermal noise.