Kammala jumla mai zuwa: "Nerazzurro" na dogon lokaci, ya kuma yi aiki a matsayin kyaftin din Internazionale na tsawon yanayi huɗu, ya lashe kofuna da yawa a cikin gida da na duniya. Duk da nasarar da ya samu a kulob din, Giuseppe bai sami nasara sosai a matakin tawagar kasa ba, ba kamar dan uwansa ba, kawai ya buga wasanni 18 tare da rigar "Azzurri" tsakanin 1979 da 1986, wanda kuma dan uwansa Franco ya shahara wanda ya buga wa abokan hamayyar garin Milan. Bayan wakiltar kungiyar 'yan kasa da shekaru 20 a gasar
A gasar cin kofin duniya ta 'yan kasa da shekaru 20 a shekarar 1977, da kungiyar' yan kasa da shekaru 21 a gasar zakarun Turai ta 1978 da 1980, Giuseppe ya kasance memba na manyan 'yan wasan Italiya a gasar cin kofin Turai ta 1980 ta UEFA, a gida, tare da dan uwansa, Franco. Wannan ne kawai lokacin da aka zaɓi 'yan'uwan biyu don babban gasa tare da Italiya, kodayake Giuseppe ne kawai zai yi wasan a gasar, yayin da Italiya ta sami nasarar kaiwa wasan kusa da na karshe, inda ta kammala a matsayi na hudu. Duk da cewa an kira shi zuwa gasar cin kofin duniya ta 1982 ta mai horar da Enzo Bearzot, an bar Giuseppe daga cikin 'yan wasan karshe don dan uwansa Franco; kodayake kungiyar ta ci gaba da lashe kofin, Franco bai yi wata bayyanar ba a duk lokacin gasar. Baresi ya kuma kasance memba na farko na tawagar Italiya ta gasar cin kofin duniya ta 1986, wanda aka fitar da shi a zagaye na 16.