There are some variables to take into account. First of all it's not trivial to just access the Linux partitions. Mainly because, natively, Windows does not support ext3 or ext4 which are used to install Linux on. Without these drivers it's impossible to access the drives. Malware will, normally, not have onboard read/write drivers for these filesystems.
While very implausible it's not impossible. To prevent your Windows partition from viewing Linux you will need to encrypt your Linux partition with LUKS. To prevent your Linux from accessing your Windows partition, you need to encrypt your Windows partition with Truecrypt (full system encryption).
The hard part here is setting it all up. I did find a nice article over here which details how you can setup such a system.