Miniature, battery-free implants promise transformative bio-electronic therapies by enabling minimally invasive implantation procedures, reducing risk, and extending device lifetime. Among all wireless power and data transfer (WPDT) modalities, magnetoelectrics (ME) has emerged as a particularly promising solution for millimeter-scale implants, boasting lower tissue attenuation and higher power transfer efficiency over conventional inductive and ultrasonic methods. However, as an acoustic resonator, ME devices face an inherent tradeoff between Q-factor and bandwidth, limiting their ability to simultaneously achieve high-speed communication and efficient wireless power transfer (WPT). To fundamentally circumvent the challenge, this paper presents dual-resonance ME WPDT that exploits the unique multimode resonances of ME transducers to realize WPT and communication at distinct frequencies. Based on this dual-resonance principle, we demonstrate reconfigurable active and passive schemes for different biomedical applications, with a proof-of-concept system including a miniature implant and an external transceiver. The active scheme achieves 60 kbps at operational distances of 6 cm with 2.5 mW implant power, while the passive backscatter offers 20 kbps continuous streaming at 4 cm with negligible power, demonstrating the first reported non-interrupted ME WPDT system and more than twice the data rate of previous ME backscatter methods. Both schemes further support on-off keying (OOK) and binary phase shift keying (BPSK) modulations, providing additional flexibility to tailor communication needs between power efficiency and robustness. The complete prototype system was validated through comprehensive in-vitro experiments and in-vivo EMG streaming in a rodent model.