Вы можете использовать Array.reduce и Array.filter
ES6 и выше
let arr = [{"Description":"xyz","items":[{"itemid":319,"itemDescription":"bucket","UnitCharge":10},{"itemid":320,"itemDescription":"mug","UnitCharge":100},{"itemid":349,"itemDescription":"Jug","UnitCharge":0}]},{"Description":"xyz2","items":[{"itemid":301,"itemDescription":"chair","UnitCharge":10},{"itemid":382,"itemDescription":"table","UnitCharge":0}]}];
let result = arr.reduce((a,c) => [...a, ...c.items.filter(v => v.UnitCharge > 0)], []);
console.log(result);
ES5
let arr = [{"Description":"xyz","items":[{"itemid":319,"itemDescription":"bucket","UnitCharge":10},{"itemid":320,"itemDescription":"mug","UnitCharge":100},{"itemid":349,"itemDescription":"Jug","UnitCharge":0}]},{"Description":"xyz2","items":[{"itemid":301,"itemDescription":"chair","UnitCharge":10},{"itemid":382,"itemDescription":"table","UnitCharge":0}]}];
let result = arr.reduce(function(a,c){
return a.concat(c.items.filter(function(v){
return v.UnitCharge > 0
}));
}, []);
console.log(result);
РЕДАКТИРОВАТЬ
let arr = [{"Description":"xyz","items":[{"itemid":319,"itemDescription":"bucket","UnitCharge":10},{"itemid":320,"itemDescription":"mug","UnitCharge":100},{"itemid":349,"itemDescription":"Jug","UnitCharge":0}]},{"Description":"xyz2","items":[{"itemid":301,"itemDescription":"chair","UnitCharge":10},{"itemid":382,"itemDescription":"table","UnitCharge":0}]}];
let result = arr.map(({items, ...rest}) => ({...rest, items:items.filter(v => v.UnitCharge > 0)}));
console.log(result);
РЕДАКТИРОВАТЬ 2
let arr = [{"Description":"xyz","items":[{"itemid":319,"itemDescription":"bucket","UnitCharge":10},{"itemid":320,"itemDescription":"mug","UnitCharge":100},{"itemid":349,"itemDescription":"Jug","UnitCharge":0}]},{"Description":"xyz2","items":[{"itemid":301,"itemDescription":"chair","UnitCharge":10},{"itemid":382,"itemDescription":"table","UnitCharge":0}]}];
let result = arr.map(({items, ...rest}) => ({...rest, items:items.filter(v => v.UnitCharge > 0)})).filter(v => v.items.length > 0);
console.log(result);