Speed-of-sound and optical absorption reflect the structure and function of tissues from different aspects. A dual-mode microscopy system based on a concentric annular ultrasound array is proposed to simultaneously acquire the long depth-of-field images of speed-of-sound and optical absorption of inhomogeneous samples. First, speed-of-sound is decoded from the signal delay between each element of the annular array. The measured speed-of-sound could not only be used as an image contrast, but also improve the resolution and accuracy of spatial location of photoacoustic image in inhomogeneous acoustic media. Secondly, benefitting from dynamic focusing of annular array and the measured speed-of-sound, it is achieved an advanced acoustic-resolution photoacoustic microscopy with a precise position and a long depth-of-field. The performance of the dual-mode imaging system has been experimentally examined by using a custom-made annular array. The proposed dual-mode microscopy might have the significances in monitoring the biological physiological and pathological processes.