Using discrete Hartley transform (DHT) instead of discrete Fourier transform (DFT) in the optical index modulation (IM) aided orthogonal frequency division multiplexing (OFDM) systems for visible light communications (VLC) results in improvement in terms of the spectral efficiency, energy efficiency, peak-to-average power ratio, and bit error rate (BER) performance with a lower computational complexity, benefiting from the removal of the Hermitian symmetry. In this paper, by employing dual-mode (DM) index modulation in the DHT-based OFDM systems, more spectral efficient schemes for VLC are proposed. A reduced-complexity maximum likelihood (ML) detector and a simple log-likelihood ratio (LLR) detector for the DM-OFDM-IM systems are presented, achieving a better performance with a lower complexity over the traditional detectors. The spectral efficiency and the average BER are analyzed. The minimum distance between different transmitted subblock vectors is calculated for characterizing the performance. The simulation results demonstrate that the DHT-based DM-OFDM-IM systems achieve significant performance gains over the DHT-based OFDM-IM counterparts and perform better than the DFT-based counterparts in terms of the spectral efficiency and BER performance.