You no longer work with jQuery objects using square brackets.
jQuery("li")[0]
This returns 1st lias a DOMElement, not a jQuery object.
jQuery("li")[0].children[0]
This returns the 1st li1st child as a DOMElement, not a jQuery object.
.html()
This function only works for jQuery objects. For DOMElements you can use a property .innerHTML.
DOMElements, jQuery. :
jQuery('li').eq(0).children().eq(0).html()