We consider a two-component Bose–Einstein condensate, which consists of both dipolar and scalar bosonic atoms, in a confinement that is composed of a harmonic oscillator and an underlying optical lattice set rotation. When the dipoles are polarized along the symmetry axis of the harmonic potential, the ground-state density distributions of such a system are investigated as a function of the relative strength between the dipolar and contact interactions, and of the rotation frequency. Our results show that the number of vortices and its related vortex structures of such a system depend strongly on such system parameters. The special two-component system considered here opens up alternate ways for exploring the rich physics of dipolar quantum gases.