Two-dimensional (2D) B-C-N alloys have recently attracted much attention but unfortunately, Chemical Vapor Deposition (CVD) B-C-N alloys typically phase separate. In spite of that, our analysis of the B-C-N alloy fabricated by electron-beam irradiation suggests that non-phase-separated B-C-N may in fact exist with a carbon concentration up to 14 at%. While this analysis points to a new way to overcome the phase-separation in 2D B-C-N, by first-principles calculations, we show that these B-C-N alloys are made of motifs with even numbers of carbon atoms, in particular, dimers or six-fold rings (in a molecule-like form), embedded in a 2D BN network. Moreover, by tuning the carbon concentration, the band gap of the B-C-N alloys can be reduced by 35% from that of BN. Due to a strong overlap of the wavefunctions at the conduction band and valance band edges, the non-phase-separated B-C-N alloys maintain the strong optical absorption of BN.