First of all, it's not jQuery vs. JavaScript. It's jQuery vs the DOM API as-is which is crufty and ugly and kind of obtuse but traditionally most-importantly, unevenly supported in a big way in Microsoft browsers before IE9. But it's all JavaScript. If you're thinking about it any other way you need to lift open the hood and learn what JQ's internals are actually doing.
And no I honestly don't see what the problem with using both is. If you're mucking with the DOM you should know the DOM. One of the things I like about jQuery is that it gets the hell out of my way. Why should I fire a method to get a property I know is available in all browsers when I can just reference it via [0].someProperty
instead for instance? Using both shouldn't make it harder for another UI dev to tweak your stuff if jQuery is in the mix because it's never going to have a problem with you doing that. At any time you can wrap any dom collection or object in a $ produced object wrapper by just tossing it in as an argument of the $ function and you're back in jQuery-land so it's not like you've made your code harder for somebody else to modify because that person was less comfortable with the native API.
But they should be able to read plain vanilla DOM API stuff if it's their business to tweak things at that level, regardless of their comfort-level using it. That's just the threshold of technical literacy for a proper entry-level UI-dev as far as I'm concerned. Generally speaking, of course, it can make code more legible to be consistent in the things that you do, but when you feel there's a sensible reason to go one way or the other, there's no reason not to. The key to making that decision is to know a lot about both.
In the scenario where somebody is really freaked out when they see a mix of things happening both the JQ way and the DOM API way, that's often a server-side dev not wanting to wade through stuff they don't really understand in order to re-use your code when you get smacked by the prodigal programmer-murdering bus. In that scenario, they shouldn't even be looking at this stuff in order to understand how to re-use your code for implementation on other pages or to set some alternate behavior. They should be looking at generic JavaScript objects, methods, and factories that expose a consistent/easily-documented API of your own for doing things like sticking a bunch of UI widgets of a given type on a page or setting all the combo boxes in a table to stop doing the auto-filtering thing when you type. All the DOM stuff should be buried and hidden from people who don't need to know it.
And that shouldn't be hard for you to do if ultimately it's all just JavaScript to you.