Hyperbolic metasurfaces (HMSs) that possess special dispersion properties have attracted immense attention owing to their capability of manipulating electromagnetic waves in the near field. However, in previous HMSs, electric and magnetic surface waves are excited and manipulated individually. Simultaneous control of electric and magnetic surface waves has not been studied, in particular, in HMSs with multiple energy bands. Here, we propose and demonstrate a 2D electromagnetic HMS that enables the propagation of both electric and magnetic surface waves by different means of terahertz radiation excitation, and there are independent self-collimation frequencies in the orthogonal directions. The experimental observations agree well with numerical simulations. The proposed HMS opens an unprecedented avenue for nondiffracting transmission and near-field focusing and shows exceptional prospects in designing planar photonic devices, hyperlenses, and waveguides.