Due to a clock config conflict, the default config does not allow Ethernet and UART3 to be used at the same. See this thread.
A workaround for Mbed projects is to disable PORTC clock in mbed-os/features/netsocket/emac-drivers/TARGET_Freescale_EMAC/TARGET_K64F/hardware_init_MK64F12.c.
// CLOCK_EnableClock(kCLOCK_PortC); // commented
CLOCK_EnableClock(kCLOCK_PortB);
/* Affects PORTC_PCR16 register */
// PORT_SetPinMux(PORTC, 16u, kPORT_MuxAlt4); // commented
/* Affects PORTC_PCR17 register */
// PORT_SetPinMux(PORTC, 17u, kPORT_MuxAlt4); // commented
/* Affects PORTC_PCR18 register */
// PORT_SetPinMux(PORTC, 18u, kPORT_MuxAlt4); // commented
/* Affects PORTC_PCR19 register */
// PORT_SetPinMux(PORTC, 19u, kPORT_MuxAlt4); // commented
/* Affects PORTB_PCR1 register */
PORT_SetPinMux(PORTB, 1u, kPORT_MuxAlt4);