JPEG-domain enhancement improves the visual quality of JPEG images by directly manipulating the decoded DCT (discrete cosine transform) coefficients, which inevitably leads to mixed compression and enhancement artifacts. Existing forensic methods that merely consider JPEG artifacts are unsuitable to address such mixed artifacts and hence suffer a considerable performance decline in compression parameter estimation and lack the ability to estimate the enhancement parameter. This work attempts to explore the characterization of the mixed artifacts, and to further estimate both the enhancement and compression parameters of JPEG-domain enhanced images. First, a statistical likelihood function is proposed to characterize the periodicity of DCT coefficients, which can measure how well an enhanced image is de-enhanced back to its JPEG compressed version given the compression and enhancement parameters. The proposed likelihood function reaches its maximum if the parameters match their true values. Then, a forensic method of enhancement detection and parameter estimation is developed based on the proposed likelihood function for two kinds of classical JPEG-domain enhancement. Specifically, JPEG-domain enhanced images are detected by thresholding a scalar feature computed upon the likelihoods, and the enhancement and compression parameters are estimated by locating the maximal likelihood. In addition, mathematical proof of the de-enhancement feasibility is provided. Experimental results demonstrate that the proposed method outperforms the compared methods in both enhancement detection and parameter estimation.