ASM1042 is often paired with ASM1051E as a chipset in order to provide 2 USB 3.0 ports as well as one SATA 6Gbps port on the same card. ASM1051E does not show up in lspci even though it is there, working. Works with gNewSense 3.0 LiveDVD and Trisquel 6.0 LiveCD out-of-the-box. I don't have any USB 3.0 devices to test with it, but USB 2.0 devices seem to work fine. SATA HDD drives can also be detected while SSDs cannot (August 2013).
Slot: 04:00.0 Class: USB controller [0c03] Vendor: ASMedia Technology Inc. [1b21] Device: ASM1042 SuperSpeed USB Host Controller  SVendor: ASUSTeK Computer Inc.  SDevice: Device  ProgIf: 30
04:00.0 USB controller [0c03]: ASMedia Technology Inc. ASM1042 SuperSpeed USB Host Controller [1b21:1042] Subsystem: ASUSTeK Computer Inc. Device [1043:8488] Kernel driver in use: xhci_hcd Kernel modules: xhci_hcd