Single word for happy and envious at the same time
Solution 1:
Not sure if such a word exists, although it should do. There are several sites which list foreign words which ought to exist in the English language. This one has several suggestions (some words are duplicated). I especially like; toska, torschlusspanik, and tingo.
I was asking my boyfriend, 100% native English speaker who probably reads close to 200 books a year, if he knew of such a word and he suggested schadenfreude, which I said was completely wrong, (in this case) and had a very negative meaning. It's when a person takes delight at somebody's misfortunes or worse, his or her downfall. Which just goes to show being a native speaker and a 100% pure-bred English man is no guarantee that you have a full comprehensive knowledge of the language, either that or he wasn't listening to me.
My first instinct would be to rephrase the sentiment in order to convey that mixed emotion you asked for.
Although happy for her success, [name] couldn't help but feel a twinge of envy.
Now, why did I change the word jealousy to envy? I don't think a person can be happy and jealous at the same time. Jealousy expresses the negative feeling that one might experience towards an object or person "possessed" by them, i.e. to be jealous of a loved one for example, a girlfriend, a husband, etc. A person who is said to be jealous of his wife is fearful of losing her to a rival; that fear may be either irrational or rational. If you are jealous of your possessions you want to guard them, and make sure no one else can have access to them. Young children are often described as being jealous of their toys.
Envy on the other hand, (for me) is a slightly less negative emotion. I can imagine myself feeling happy for another person's good fortune or success and be unintentionally envious at the same time. I wish I could possess that same object of desire, the same fortune, the same success. I can be envious of a neighbour's new car, a colleague's promotion, or a friend's idyllic family etc.
To lessen or diminish the gravity of that emotion I may add in increasing order of quantity: a bit, a twinge, a pang or a stab.
Solution 2:
I think I have an answer for you on this one. My friend worked with Upic Eskimos in the 80's and brought back a word that I have been spreading for 20 plus years. He described it as being happy for someone but also jealous. I found your thread when I was trying to figure out how to spell it. The Word is "Cha-Wuk-Tah". The "Wuk" is said with a slight clearing of the throat sound, as in "Waachh". The spelling might be "Chawachtah", but that's just a guess. It's a great word.