The renormalization-group recursion relations obtained by Chen and Lubensky for the multicritical point associated with simultaneous critical fluctuations in both the spin-glass and ferromagnetic order are reanalyzed. To first order in ε==6-d we find that the multicritical fixed point is located inside the Nishimori manifold and that the scaling axes agree with those obtained recently from general arguments. It is confirmed that the scaling along the Nishimori line and at the paramagnetic-spin-glass transition are related. We also point out some universal properties of the multicritical point of possible experimental interest.