Digital images in the real world are created by a variety of means and have diverse properties. A photographical natural scene image (NSI) may exhibit substantially different characteristics from a computer graphic image (CGI) or a screen content image (SCI). This casts major challenges to objective image quality assessment, for which existing approaches lack effective mechanisms to capture such content type variations, and thus are difficult to generalize from one type to another. To tackle this problem, we first construct a cross-content-type (CCT) database, which contains 1,320 distorted NSIs, CGIs, and SCIs, compressed using the high efficiency video coding (HEVC) intra coding method and the screen content compression (SCC) extension of HEVC. We then carry out a subjective experiment on the database in a well-controlled laboratory environment. Moreover, we propose a unified content-type adaptive (UCA) blind image quality assessment model that is applicable across content types. A key step in UCA is to incorporate the variations of human perceptual characteristics in viewing different content types through a multi-scale weighting framework. This leads to superior performance on the constructed CCT database. UCA is training-free, implying strong generalizability. To verify this, we test UCA on other databases containing JPEG, MPEG-2, H.264, and HEVC compressed images/videos, and observe that it consistently achieves competitive performance.