You should have no problem with that at all, at least on the Intel chipset.
Actually, using a standard HDD on a SATA III port, even if it a so called "SATA 6Gb/s" HDD, is a waste of the SATA III port. Not one HDD can even use the full potential of a SATA II port, so no point in using a SATA III port for a HDD. Doing things as you described may even be isolating the SSD from the RAID 5 volume, since I think the SATA III ports are provided by a separate portion of the Z77 chipset. Regardless, do it as you described.
About the ASMedia chipset, some of the third party chips like the Marvell, do not work with ATAPI devices like a DVD drive. The ASMedia may not be in that category, so just try. I have a feeling that the problem actually is the lack of a driver for the secondary chipsets when an OS installation is being done.
If you are installing an OS on that system, via a disk, I would put the BluRay drive on an Intel SATA II port, and only have the SSD connected, no other drives. After the OS is installed, then move the BluRay to the ASMedia ports, and create your RAID 5 volume.