In-band full-duplex (IBFD) operation is essential for both sensing-centric and communication-centric integrated sensing and communications (ISAC) systems. Both types require the monostatic transceiver to overcome the technical challenge of self-interference (SI). To address this challenge, a photonics-assisted self-interference cancellation (SIC) scheme for an IBFD ISAC transceiver is proposed and experimentally demonstrated. By utilizing wavelength division multiplexing, the SI is cancelled by a cancellation reference with matched amplitude and time delay, using two counter-biased Mach-Zehnder modulators. In proof-of-concept experiments, the proposed IBFD ISAC transceiver is tested using a 10 GHz quadrature amplitude modulation (QAM) constant envelope linear frequency modulation orthogonal frequency division multiplexing (CE-LFM-OFDM) ISAC signal with a carrier frequency and a bandwidth of 10 GHz and 2 GHz, respectively. Experimental results show that cancellation depths of 35.29 dB and 32.59 dB are achieved with bandwidths of 1 GHz and 2 GHz, respectively, in the communication receiver. The corresponding weak signal of interest is successfully recovered after effective SIC in the wireless link. The ranging and imaging functions are also experimentally verified. The experimental results show that the cancellation depth of the SI after de-chirping is 23.6 dB when the center frequency and bandwidth of the CE-LFM-OFDM RF signal are 10 GHz and 2 GHz, respectively. A dynamic range increase of 23.84 dB is achieved in imaging function. The corresponding radar ranging resolution of 10 cm is also achieved for radar function. The proposed scheme cancels the SI in both communication and radar receivers, demonstrating excellent performance in the IBFD ISAC transceiver system.