With the advent and rapid development of the transformation optics and metamaterials, invisibility cloaks have captivated much attention in recent years. While most cloaking schemes suffer from limited bandwidth, the carpet cloak, which can hide an object on a reflecting plane, can operate over a broadband frequency range. However, the carpet cloaks experimentally realized thus far still have several limitations. For example, the quasi-conformal mapping carpet cloak leads to a lateral shift of the reflected light ray, while the birefringent carpet cloak only works for a specific polarization. In this work, we propose a conformal transformation scheme to tackle these two problems simultaneously. As an example, we design a mid-infrared carpet cloak in a silicon platform and demonstrate its polarization-insensitive property as well as the minimized lateral shift over a broad frequency band from 24 to 28.3 THz.