Planets in our solar system have strikingly different chemical compositions - the four rocks closest to the sun (Mercury, Venus, Earth, Mars) have most of their mass made up of rocky and metallic elements (the centre of the Earth is mainly nickel and iron), whereas the gas giants of Jupiter and Saturn are made up of much lighter and simpler elements (mainly Hydrogen and Helium)
Jupiter has hydrogen all the way to its core, where pressures are so intense that a form of 'metallic hydrogen' is thought to exist there. So yes, there are less step-changes in elemental composition and therefore less step-changes in density - however, density step-changes still do exist where matter (even the same elements) exists in different states under different conditions - e.g. gas, liquid and possibly metallic hydrogen at different pressures and temperatures - that. That is a feature of chemistry.
The reason for the elemental difference in the planets is partly due to the make-up and distribution within the accretion disk, the swirl of elements that existed when our solar system formed. Also, planets that are as big as Jupiter have such a strong gravitational pull that they are able to hold onto (and pull in more) of the lighter elements like hydrogen and helium, which are the most abundant in the universe. Jupiter is actually like a half-there star, sometimes referred to as a 'failed star'.
However, the Earth is still large enough and has a protective magnetic shield generated by its iron core that allows its atmosphere not to be blasted away by the solar wind. This means we have both a sizeable stable gaseous atmosphere as well as a metallic and rocky interior, meaning a big step-change in densities between solids and gases.
It is also worth noting though that our gaseous atmosphere is only 60 miles thick, whereas the Earth's radius is about 4,000 miles. The planet is much more of a homogenous solid than you might think, being as we are atmosphere dwellers.