Mid-infrared (MIR) microcomb provides a new way into the "molecular fingerprint" region. However, it remains rather a challenge to realize the broadband mode-locked soliton microcomb, which is often limited by the performance of available MIR pump sources and coupling devices. Here, we propose an effective approach towards broadband MIR soliton microcombs generation via a direct pump in the near-infrared (NIR) region, through full utilization of the second- and third-order nonlinearities in a thin-film lithium niobate microresonator. The optical parametric oscillation process contributes to conversion from the pump at 1550 nm to the signal around 3100 nm, and the four-wave mixing effect promotes spectrum expansion and mode-locking process. While the second-harmonic and sum-frequency generation effects facilitate simultaneous emission of the NIR comb teeth. Both the continuous wave and pulse pump sources with relatively low power can support a MIR soliton with a bandwidth over 600 nm and a concomitant NIR microcomb with a bandwidth of 100 nm. This work can provide a promising solution for broadband MIR microcombs by breaking through the limitation of available MIR pump sources, and can deepen the understanding of the physical mechanism of the quadratic soliton assisted by the Kerr effect.