It is clear from the way in which Huck and Jim's life is presented in chapters such as Chapter 19 for example, when they are by themselves and living happily and in perfect tranquility, at one with nature, that the prime desire that both characters want is a simple, quiet life, free from the worries and pressures of civilisation. Note the way their lives are described at the beginning of this chapter:
Not a sound anywheres--perfectly still--just like the whole world was asleep, only sometimes the bullfrogs a-cluttering, maybe. The first thing to see, looking away over the water, was a kidn of dull line--that was the woods on t'other side; you couldn't make nothing else out; then a pale place in the sky; then more paleness spreading around; then the river softened up away off, and warn't black any more, but grey; you could see the little dark spots drifting along ever so far away...
Such passages create images of beauty and wonder as Jim and Huck live off of the land and are separate from other humans and the "civilisation" that only seems to bring them such problems. They live at peace with each other and with nature, and it is only the frequent and unwelcome contact that they make with "civilisation" that disrupts this idyllic image. Thus principally Jim and Huck share a desire for peace and have a common value of the importance of nature and what humanity in its "civilisation" actually represents.