I don't really understand how SDHC controller work, so my question is : is it possible to use SDHC controller as simple SPI interface with multiple data lines?
Not really possible...
The SDHC interface is basically 4 SPI lines in parallel when viewed from the perspective of the SD Simplified physical layer specs - the commands / data are split over 4 lines, and CRC'd individually. The SDHC takes care of this for you though. I believe to develop code for 4 wire SDIO access rather than SPI, you have to join the SD card developers group though.
The SDHC interface as connected on the K60 tower kit does allow single wire SPI access to the SD card though.
I'll leave this below as I misread the question and people might find the following useful:
Yes it is possible. If you look on the schematics you will find:
SD Pin...Port...MCU function:
I'm assuming SIN / SOUT refers to slave in, slave out. Therefore SIN is the MCU output, SOUT is the MCU input. SPI1_PCS0 I assume stands for "peripheral chip select". There are several of these so you can have SPI1 talking to several slave devices.
So, using SPI1, you can talk to the SD card in SPI mode, on the K60 twr kit. Handy.