Grammar JLPT Level N4 - Lesson 29

The conjunction それに is regularly considered to be one word in Japanese, but is more correctly just a combination of the pronoun それ, and the case marking particleに.
The thing that それ is 'substituting' for is the entire clause/sentence that came before it, while に highlights that extra information is about to be added. In this way, it translates to 'and to that', or 'and on that', where 'that' is the previous information. Often, it is translated simply as 'moreover', 'in addition', or 'and'.

• それに彼(かれ)は家事(かじ)もしないんでしょう？
  In addition, he doesn't do house chores either, right?
• リサの会社(かいしゃ)には残業(ざんぎょう)がない。それに給料(きゅうりょう)もいい。
  Lisa's company doesn't have overtime work. What's more, her salary is good too.

Because それに is 'adding' information with に, the (B) information itself must be something that would logically happen 'in addition to (A)', or 'as a result of (A)'. Therefore, それに will highlight something that has either all positive, or all negative connotations. Never both.

• 昨日(きのう)、道(みち)で5千円(せんえん)を拾(ひろ)って、それに車(くるま)が抽選(ちゅうせん)で当(あ)たった！
  Yesterday, I picked up 5 thousand yen on the street, and in addition to that I won a car in the lottery. (Natural Japanese, as both events are positive)
• 最近(さいきん)は雨(あめ)がいっぱい降(ふ)るし、それに風(かぜ)も強(つよ)いし、外(そと)に出(で)れなくて寂(さび)しい。
  Recently, it has been raining a lot, and in addition to that the wind has been strong. I'm sad that I can't go outside. (Natural Japanese, as both events are negative)
• 今朝(けさ)はマッサージに行(い)って、それにスピード違反(いはん)の切符(きっぷ)も切(き)られた。
  I went to get a massage this morning, and moreover I also got a speeding ticket. (Unnatural Japanese, as one event is positive, while the other is negative)