Transmission spectroscopy provides a powerful probe of the atmospheric properties of transiting exoplanets. To date, studies of exoplanets in transit have focused on inferring their atmospheric properties such as chemical compositions, cloud/haze properties, and temperature structures. However, surface inhomogeneities in the host stars of exoplanets in the form of cool spots and hot faculae can in principle imprint signatures on the observed planetary transit spectrum. Here we present Aura, a new retrieval paradigm for inferring both planetary and stellar properties from a transmission spectrum. We apply our retrieval framework to a sample of hot giant exoplanets to determine the significance of stellar heterogeneity and clouds/hazes in their spectra. The retrieval analyses distinguish four groups of planets. First, the spectra of WASP-6b and WASP-39b are best characterised by imprints of stellar heterogeneity and hazes and/or clouds. HD 209458b and HAT-P-12b comprise the second group for which there is weak evidence for stellar heterogeneity and a high significance of hazes and/or clouds. The third group constitutes HAT-P-1b and WASP-31b and shows weak evidence against stellar heterogeneity but weak to substantial indications of clouds/hazes. The fourth group -- WASP-19b, WASP-17b, and WASP-12b -- is fit best by molecular and alkali absorbers with H$2$ scattering without evidence for stellar heterogeneity and weak to no evidence for clouds/hazes. Our retrieval methodology paves the way to simultaneous information on the star and planet from higher resolution spectra using future facilities such as the James Webb Space Telescope and large ground-based facilities.