Road surface profile (RSP) estimation is an important task to find the imperfections of a road surface, thereby improving ride quality. The RSP estimation has been recently studied using stereo vision owing to its affordable price. However, the existing methods provide noisy and temporally unstable results for real-world driving scenes because of noisy range measurements, noisy pitch angle estimates between the camera and the road surface, and interference from obstacles. This paper proposes a novel method for temporally consistent and robust RSP estimation to overcome these problems. The proposed method consists of three steps: free space estimation, digital elevation map (DEM) estimation, and RSP estimation. We first estimate a drivable area, i.e., free space. For robust and fast free space estimation, we propose an optimization-based non-parametric road surface modeling method and an integral disparity histogram-based free space estimation method. Then, the DEM of the road surface is estimated using range measurements on the free space to avoid obstacle interference. The DEM is temporally updated every frame using the moving average filter and the DEM reference grid update scheme. Owing to these strategies, the proposed method reduces the elevation estimation noise and the pitch angle error, and therefore provides the temporally consistent RSP. We demonstrate the superiority of the proposed method experimentally using stereo image sequences captured in real-world driving scenes.