In the FAME! Project, a code-switching (CS) automatic speech recognition (ASR) system for Frisian-Dutch speech is developed that can accurately transcribe the local broadcaster's bilingual archives with CS speech. This archive contains recordings with monolingual Frisian and Dutch speech segments as well as Frisian-Dutch CS speech, hence the recognition performance on monolingual segments is also vital for accurate transcriptions. In this work, we propose a multi-graph decoding and rescoring strategy using bilingual and monolingual graphs together with a unified acoustic model for CS ASR. The proposed decoding scheme gives the freedom to design and employ alternative search spaces for each (monolingual or bilingual) recognition task and enables the effective use of monolingual resources of the high-resourced mixed language in low-resourced CS scenarios. In our scenario, Dutch is the high-resourced and Frisian is the low-resourced language. We therefore use additional monolingual Dutch text resources to improve the Dutch language model (LM) and compare the performance of single- and multi-graph CS ASR systems on Dutch segments using larger Dutch LMs. The ASR results show that the proposed approach outperforms baseline single-graph CS ASR systems, providing better performance on the monolingual Dutch segments without any accuracy loss on monolingual Frisian and code-mixed segments.