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The concurrent execution of deep neural networks (DNN) inference tasks on intermittently-powered batteryless devices (IPDs) has recently garnered much attention due to its potential in a broad range of smart sensing applications. While the checkpointing mechanisms (CMs) provided by the state-of-the-art make this possible, scheduling inference tasks on IPDs is still a complex problem due to significant performance variations across DNN layers and CM choices. This complexity is further accentuated by dynamic environmental conditions and inherent resource constraints of IPDs. To tackle these challenges, we present MII, a framework designed for intermittence-aware inference and scheduling on IPDs. MII formulates the shutdown and live time functions of an IPD from profiling data, which our offline intermittence-aware search scheme uses to find optimal layer-wise CMs for each task. At runtime, MII enhances job success rates by dynamically making scheduling decisions to mitigate workload losses from power interruptions and adjusting these CMs in response to actual energy patterns. Our evaluation demonstrates the superiority of MII over the state-of-the-art. In controlled environments, MII achieves an average increase of 21% and 39% in successful jobs under stable and dynamic energy patterns. In real-world settings, MII achieves 33% and 24% more successful jobs indoors and outdoors.