We present a detailed analysis of the ionization and thermal structure of the intergalactic medium (IGM) around a high-redshift (z = 10) QSO, using a large suite of cosmological, multifrequency radiative transfer simulations, exploring the contribution from galaxies as well as the QSO, and the effect of X-rays and secondary ionization. We show that in high-z QSO environments both the central QSO and the surrounding galaxies concertedly control the reionization morphology of hydrogen and helium and have a non-linear impact on the thermal structure of the IGM. A QSO imprints a distinctive morphology on H II regions if its total ionizing photon budget exceeds that of the surrounding galaxies since the onset of hydrogen reionization; otherwise, the morphology shows little difference from that of H II regions produced only by galaxies. In addition, the spectral shape of the collective radiation field from galaxies and QSOs controls the thickness of the I-fronts. While a UV-obscured QSO can broaden the I-front, the contribution from other UV sources, either galaxies or unobscured QSOs, is sufficient to maintain a sharp I-front. X-ray photons from the QSO are responsible for a prominent extended tail of partial ionization ahead of the I-front. QSOs leave a unique imprint on the morphology of He II/He III regions. We suggest that, while the physical state of the IGM is modified by QSOs, the most direct test to understand the role of galaxies and QSOs during reionization is to perform galaxy surveys in a region of sky imaged by 21 cm tomography.