Integrated Sensing and Communication (ISAC) has been identified as a key 6G application by ITU and 3GPP. A realistic, standard-compatible channel model is essential for ISAC system design. To characterize the impact of Sensing Targets (STs), 3GPP defines ISAC channel as a combination of target and background channels, comprising multipath components related to STs and those originating solely from the environment, respectively. Although the background channel does not carry direct ST information, its accurate modeling is critical for evaluating sensing performance, especially in complex environments. Existing communication standards characterize propagation between separated transmitter (Tx) and receiver (Rx). However, modeling background channels in the ISAC monostatic mode, where the Tx and Rx are co-located, remains a pressing challenge. In this paper, we firstly conduct ISAC monostatic background channel measurements for an indoor scenario at 28 GHz. Realistic channel parameters are extracted, revealing pronounced single-hop propagation and discrete multipath distribution. Inspired by these properties, a novel stochastic model is proposed to characterizing the ISAC monostatic background channel as the superposition of sub-channels between the monostatic Tx&Rx and multiple communication Rx-like Reference Points (RPs). This model is compatible with standardizations, and a 3GPP-extended implementation framework is introduced. Finally, a genetic algorithm-based method is proposed to extract the optimal number and placement of multi-RPs. The optimization approach and modeling framework are validated by comparing measured and simulated channel parameters. Results demonstrate that the proposed model effectively captures monostatic background channel characteristics, addresses a critical gap in ISAC channel modeling, and supports 6G standardization.