Chartjs-Position of the x-axis labels is not in sync with the line chart data points

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The problem is that all date values correspond to the last day of a month. I added the function toFirstDayOfMonth in your code sample to further transform the data in order to obtain the expected result.

function toFirstDayOfMonth(dateString) {
  const date = new Date(dateString);
  date.setDate(1);
  return date;
}

Alternatively you could also write this function as follows to only consider the year and month of your date string.

function toFirstDayOfMonth(dateString) {      
  return new Date(dateString.substring(0, 7));
}

Please have a look at the amended code.

const data = [{
    name: "series1",
    series: [{
            date: "2016-01-31T00:00:00.000Z",
            value: 8
        },
        {
            date: "2016-02-28T00:00:00.000Z",
            value: 10
        },
        {
            date: "2016-03-31T00:00:00.000Z",
            value: 12
        },
        {
            date: "2016-04-30T00:00:00.000Z",
            value: 15
        },
         {
            date: "2016-05-31T00:00:00.000Z",
            value: 14
        },
        {
            date: "2016-06-30T00:00:00.000Z",
            value: 16
        },
        {
            date: "2016-07-31T00:00:00.000Z",
            value: 17
        }
    ]
}, {
    name: "series2",
    series: [{
            date: "2016-01-31T00:00:00.000Z",
            value: 5
        },
        {
            date: "2016-02-28T00:00:00.000Z",
            value: 7
        },
        {
            date: "2016-03-31T00:00:00.000Z",
            value: 10
        },
        {
            date: "2016-04-30T00:00:00.000Z",
            value: 13
        },
         {
            date: "2016-05-31T00:00:00.000Z",
            value: 12
        },
        {
            date: "2016-06-30T00:00:00.000Z",
            value: 14
        },
        {
            date: "2016-07-31T00:00:00.000Z",
            value: 15
        }       
    ]
}];

function toFirstDayOfMonth(dateString) {
  const date = new Date(dateString);
  date.setDate(1);
  return date;
}

new Chart(document.getElementById('myChart'), {
    type: 'line',
    data: {
        datasets: [
          {
              label: data[0].name,
              fill: false,
              backgroundColor: 'red',
              borderColor: 'red',
              data: data[0].series.map(x => ({ x: toFirstDayOfMonth(x.date), y: x.value }))
          }, {
              label: data[1].name,
              fill: false,
              backgroundColor: 'green',
              borderColor: 'green',
              data: data[1].series.map(x => ({ x: toFirstDayOfMonth(x.date), y: x.value }))
          }
        ]
    },
    options: {
        responsive: true,
        title: {
            display: false
        },
        legend: {
            display: true
        },
        tooltips: { 
            mode: 'x'
        },
        scales: {
            xAxes: [{
                type: 'time',
                distribution: 'series',
                time: {
                    unit: 'month',
                    tooltipFormat: 'MMM YYYY'
                }
            }]            
        }
    }
});
<script src="https://cdnjs.cloudflare.com/ajax/libs/moment.js/2.4.0/moment.min.js"></script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/Chart.js/2.9.3/Chart.min.js"></script>
<canvas id="myChart" height="90"></canvas>

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