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Jeny kochany is a mild euphemistic curse used instead of Jezu kochany (dearJesus). Taking the Lord's name in vain was once a serious misdeed and/or faux pas, so similar-sounding formulations were concocted instead.
Other common Polish euphemisms include: ja pierniczę (pierdolę), kurczę (kurwa), mam to w nosie (w dupie); pocałuj mnie tam, gdzie słońce nie świeci (w dupę), etc.
English is full of such euphemisms: Gosh instead of God, geez (Jesus), blimey (God blind me), cripes (Christ), goldarnit (God dammit), son of a gun (son of a *****), etc.