I'm looking for a word, doesn't have to be English, that expresses the complex emotion of being sincerely happy for someone and a bit jealous at the same time.
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.
There are 2 terms for envy. Malicious envy and benign envy.
Malicious: "If you feel other people’s successes are achieved by manipulation or because of unfair circumstances, you might find yourself wishing something bad would happen to strip them of their advantaged positions." http://everydaylife.globalpost.com/not-jealous-others-success-13972.html
Benign: "When you feel the other person’s success is well-deserved, your jealousy often serves to motivate you to do better. In this case, you can regard your envy as a positive emotion that inspires you to work harder and aim higher. If you feel you are underperforming, then turn your focus to your own behaviors rather than on the other person's achievements."
"Recent research indeed confirms that there are two types of envy: benign envy, a non-malicious form aimed at improving one’s own situation, and malicious envy aimed at pulling down the envied person". http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3356518/pdf/11031_2011_Article_9235.pdf
Maybe not a single word, but you could add a slightly negative adjective to "admiration".
While it does not always explicitly convey sincere happiness, the term emulate, as in a wish to emulate may come close to the overall intent
to copy someone’s behavior or try to be like someone else because you admire or respect that person:
Officials are looking to emulate successful ideas from other cities.
He just wants to emulate his dad.
The positive aspects of admire suggests that you are at least pleased with the person admired, if not joyously happy. The limitation is that admiration may be done at a distance and sincere happiness usually requires some closer relationship.