I think you're a bit confused about the SATA port options on your board, which is not surprising given the description of its specifications, or maybe a typo on your part. To review:
Intel SATA controller on Z77 chipset: Two SATA 6Gb/s ports, and four SATA 3Gb/s ports. RAID support: RAID 0, RAID 1, RAID 5, RAID 10, on ALL Intel ports.
ASMedia 1061 SATA chipset: Four SATA 6Gb/s ports. RAID support: None. AHCI and IDE only.
The Intel SATA 6Gb/s ports are the best performing (in benchmarks) SATA interface on any mother board. The ASMedia SATA 6Gb/s ports are much worse (in benchmarks) in performance compared to the Intel. In real world performance, the Intel SATA interface is superior to the ASMedia. Due to the nature of the ASMedia SATA chipset, using only one PCIe lane per chip, at 5Gb/s max (yes, five Gb/s, and shared by all four ports), the more drives on that interface, the slower it becomes.
I use Intel 520's, and also have a SATA 6Gb/s HDD. I would connect your drives like this:
Intel 520 on one Intel 6Gb/s port. Your two HDDs in RAID 1 on the Intel SATA 3Gb/s ports.
When I tested my "SATA 6Gb/s" HDD, I found it did not even come close to the real world SATA 3Gb/s speed of ~250MB/s sequential read. Actually, it was only a little more than half that speed, ~130MB/s. So called SATA 6Gb/s HDDs are a marketing scam IMO, they apparently meet a protocol spec so may be called SATA 6Gb/s, but they don't perform at anywhere near that speed. I must say I used a tough benchmark, AS SSD, on the HDD, but I can assure you that even if the sequential read and write speeds of your HDD were at 250MB/s, the other (more) important aspects of performance like small file (4K) read/write, access times, etc, are barely any higher than a SATA 3Gb/s HDD, sorry to say.
Bottom line, it's a waste to use the HDDs on a SATA 6Gb/s interface, if you have a SATA 6Gb/s SSD, IMO.
The good news is, you can try your drives on the various Intel and ASMedia ports, with some restrictions, and see how they work. You can create your RAID 1 array on the Intel SATA 3Gb/s ports, and move them to the SATA 6Gb/s ports for testing, or vice versa. I would suggest a BIOS clear and reset to the necessary settings (RAID is not a default) when you do that, but otherwise the RAID volume will work fine.
I would not install your OS on the SSD on the ASMedia ports, much easier and better to use the Intel ports. After the OS is installed, you can install the ASMedia driver, or just use the default Windows 7 msahci driver, but always use AHCI mode on the ASMedia chipset. Then you can try the SSD on the ASMedia SATA ports.