Due to its excellent performance in rate and resolution, fully-digital (FD) massive multiple-input multiple-output (MIMO) antenna arrays has been widely applied in data transmission and direction of arrival (DOA) measurements, etc. But it confronts with two main challenges: high computational complexity and circuit cost. The two problems may be addressed well by hybrid analog-digital (HAD) structure. But there exists the problem of phase ambiguity for HAD, which leads to its low-efficiency or high-latency. Does exist there such a MIMO structure of owning low-cost, low-complexity and high time efficiency at the same time. To satisfy the three properties, a novel heterogeneous hybrid MIMO receiver structure of integrating FD and heterogeneous HAD ($\rm{H}^2$AD-FD) is proposed and corresponding multi-modal (MD)-learning framework is developed. The framework includes three major stages: 1) generate the candidate sets via root multiple signal classification (Root-MUSIC) or deep learning (DL); 2) infer the class of true solutions from candidate sets using machine learning (ML) methods; 3) fuse the two-part true solutions to achieve a better DOA estimation. The above process form two methods named MD-Root-MUSIC and MDDL. To improve DOA estimation accuracy and reduce the clustering complexity, a co-learning-aided MD framework is proposed to form two enhanced methods named CoMDDL and CoMD-RootMUSIC. Moreover, the Cramer-Rao lower bound (CRLB) for the proposed $\rm{H}^2$AD-FD structure is also derived. Experimental results demonstrate that our proposed four methods could approach the CRLB for signal-to-noise ratio (SNR) > 0 dB and the proposed CoMDDL and MDDL perform better than CoMD-RootMUSIC and MD-RootMUSIC, particularly in the extremely low SNR region.